Truncated Perron formula
= Truncated Perron formula
{c}
A truncated Perron integral over $c-iT$ to $c+iT$ recovers a summatory function with an error controlled by
$$
\sum_n |a_n|\left(\frac xn\right)^c
\min\left(1,\frac1{T|\log(x/n)|}\right).
$$
= Truncated Perron formula
{c}
A truncated Perron integral over $c-iT$ to $c+iT$ recovers a summatory function with an error controlled by
$$
\sum_n |a_n|\left(\frac xn\right)^c
\min\left(1,\frac1{T|\log(x/n)|}\right).
$$